243/242: Difference between revisions

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Tempering it out in the full 11-limit leads to the rastmic temperament, enabling [[rastmic chords]], or, in the 2.3.11 subgroup, the [[Subgroup temperaments #Neutral|neutral]] temperament, enabling [[Neutral tetrad|neutral chords]].

=== Rastmic ~~temperament~~ ===

=== Rastmic ===

Subgroup: 2.3.5.7.11

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[[Mapping]]: [{{val| 1 1 0 0 2 }}, {{val| 0 2 0 0 5 }}, {{val| 0 0 1 0 0 }}, {{val| 0 0 0 1 0}}]

[[POTE ~~generator~~]]s: ~11/9 = 350.5254, ~5/4 = 386.1653, ~7/4 = 968.6464

[[POTE tuning]]: ~11/9 = 350.5254, ~5/4 = 386.1653, ~7/4 = 968.6464

{{Val list|legend=1| 7d, 10, 14c, 17c, 24, 27e, 31, 41, 58, 72, 130, 202 }}

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[[Badness]]: 0.05088 × 10<sup>-6</sup>

=== Neutral ~~temperament~~ ===

=== Neutral ===

Subgroup: 2.3.11

[[Comma list]]: 243/242

[[~~Lp_tuning~~|~~POL2 generator~~]]: ~~~11/9 = 350.525~~

[[Sval]] [[mapping]]: [{{val| 1 1 2 }}, {{val| 0 2 5 }}]

[[Gencom]] [[mapping]]: [{{val| 1 1 0 0 2 }}, {{val| 0 2 0 0 5 }}]

Gencom: [2 11/9; 243/242]

~~Gencom mapping:~~ [~~<1 1 0 0 2|, <0 2 0 0 5|~~]

[[POTE tuning]]: ~11/9 = 350.525

~~Map~~: ~~[<1 1 2|, <0 2 5|]~~

~~EDOs:~~ 7, 10, 17, 24~~, 41~~, 65, 89, 202, 291, 380

[[~~Tp_tuning~~#T2 tuning|RMS error]]: 0.3021 cents

[[Tp tuning #T2 tuning|RMS error]]: 0.3021 cents

== See also ==

* [[Rank-4 temperament]]

* [[Rastmic temperaments]], a collection of rank-3 temperaments where it is tempered out

* [[Rastmic chords]]

@@ Line 15: / Line 15: @@
 Tempering it out in the full 11-limit leads to the rastmic temperament, enabling [[rastmic chords]], or, in the 2.3.11 subgroup, the [[Subgroup temperaments #Neutral|neutral]] temperament, enabling [[Neutral tetrad|neutral chords]].
-=== Rastmic temperament ===
+=== Rastmic ===
 Subgroup: 2.3.5.7.11
@@ Line 23: / Line 22: @@
 [[Mapping]]: [{{val| 1 1 0 0 2 }}, {{val| 0 2 0 0 5 }}, {{val| 0 0 1 0 0 }}, {{val| 0 0 0 1 0}}]
-[[POTE generator]]s: ~11/9 = 350.5254, ~5/4 = 386.1653, ~7/4 = 968.6464
+[[POTE tuning]]: ~11/9 = 350.5254, ~5/4 = 386.1653, ~7/4 = 968.6464
 {{Val list|legend=1| 7d, 10, 14c, 17c, 24, 27e, 31, 41, 58, 72, 130, 202 }}
@@ Line 29: / Line 28: @@
 [[Badness]]: 0.05088 × 10<sup>-6</sup>
-=== Neutral temperament ===
+=== Neutral ===
 Subgroup: 2.3.11
 [[Comma list]]: 243/242
-[[Lp_tuning|POL2 generator]]: ~11/9 = 350.525
+[[Sval]] [[mapping]]: [{{val| 1 1 2 }}, {{val| 0 2 5 }}]
+[[Gencom]] [[mapping]]: [{{val| 1 1 0 0 2 }}, {{val| 0 2 0 0 5 }}]
 Gencom: [2 11/9; 243/242]
-Gencom mapping: [&lt;1 1 0 0 2|, &lt;0 2 0 0 5|]
+[[POTE tuning]]: ~11/9 = 350.525
-Map: [&lt;1 1 2|, &lt;0 2 5|]
-EDOs: 7, 10, 17, 24, 41, 65, 89, 202, 291, 380
+{{Val list|legend=1| 7, 10, 17, 24, 65, 89, 202, 291, 380 }}
-[[Tp_tuning#T2 tuning|RMS error]]: 0.3021 cents
+[[Tp tuning #T2 tuning|RMS error]]: 0.3021 cents
 == See also ==
+* [[Rank-4 temperament]]
 * [[Rastmic temperaments]], a collection of rank-3 temperaments where it is tempered out
 * [[Rastmic chords]]